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Model discovery of compartmental models with Graph-Supported Neural Networks

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  • Aguilar-Canto, Fernando Javier
  • Brito-Loeza, Carlos
  • Calvo, Hiram

Abstract

In this proposal, our objective is to create a neural network for the discovery of models using compartmental models as systems of Ordinary Differential Equations (ODEs), employing Graph-Supported Neural Networks (GSNN). We design the GSNN as a graph of transition functions of the structure of the model to ensure that the three properties of the ODE solution are satisfied: additivity to one, positivity, and boundness. Rather than directly estimating the solution, these neural networks approximate the transition functions. We present theoretical evidence substantiating that our GSNN maintains these properties, along with approximation outcomes from both simulated and real-world data. These outcomes demonstrate that our GSNN outperforms the non-graph-supported approach for these issues, with instances where it even surpasses full model-based solutions and Recurrent Neural Networks. Furthermore, an evolutionary algorithm successfully generated a consistent model using the data, offering a comprehensive framework for neural network-based model discovery in these scenarios.

Suggested Citation

  • Aguilar-Canto, Fernando Javier & Brito-Loeza, Carlos & Calvo, Hiram, 2024. "Model discovery of compartmental models with Graph-Supported Neural Networks," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    • Handle: RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005611
    DOI: 10.1016/j.amc.2023.128392
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    References listed on IDEAS

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    1. Yinghao Chen & Hanyu Yu & Xiangyu Meng & Xiaoliang Xie & Muzhou Hou & Julien Chevallier, 2021. "Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network," Post-Print halshs-04250266, HAL.
    2. Bryan C Daniels & Ilya Nemenman, 2015. "Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-14, March.
    3. Volodymyr Mnih & Koray Kavukcuoglu & David Silver & Andrei A. Rusu & Joel Veness & Marc G. Bellemare & Alex Graves & Martin Riedmiller & Andreas K. Fidjeland & Georg Ostrovski & Stig Petersen & Charle, 2015. "Human-level control through deep reinforcement learning," Nature, Nature, vol. 518(7540), pages 529-533, February.
    4. Luís F. Seoane & Xaquín Loredo & Henrique Monteagudo & Jorge Mira, 2019. "Is the coexistence of Catalan and Spanish possible in Catalonia?," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-9, December.
    5. Daniel M. Abrams & Steven H. Strogatz, 2003. "Modelling the dynamics of language death," Nature, Nature, vol. 424(6951), pages 900-900, August.
    6. Bryan C. Daniels & Ilya Nemenman, 2015. "Automated adaptive inference of phenomenological dynamical models," Nature Communications, Nature, vol. 6(1), pages 1-8, November.
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